Question 316593
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ =\ x_4\ +\ x_5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_2\ =\ x_1\ +\ x_3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ =\ x_2\ -\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_4\ =\ x_3\ +\ 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ +\ x_2\ +\ x_3\ +\ x_4\ +\ x_5\ =\ 23]


============


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_2\ =\ x_2\ -\ 1\ +\ x_3\ \rightarrow\ x_3\ =\ 1]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_4\ =\ x_3\ +\ 2\ =\ 1\ +\ 2\ =\ 3]


Substituting what we know so far:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ +\ x_2\ +\ 1\ +\ 3\ +\ x_5\ =\ 23]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ +\ x_2\ +\ x_5\ =\ 19]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ =\ 3\ +\ x_5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_2\ =\ x_1\ +\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_2\ =\ 3\ +\ x_5\ +\ 1\ =\ x_5\ +\ 4\ \ \rightarrow\ \ x_5\ =\ x_2\ -\ 4]


Substituting again:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ +\ 2x_2\ -\ 4\ =\ 19\ \rightarrow\ x_1\ +\ 2x_2\ =\ 23]


But since


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ =\ x_2\ -\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ +\ 2x_2\ =\ 23\ \rightarrow\ 3x_2\ -\ 1\ =\ 23\ \rightarrow\ 3x_2\ =\ 24\ \rightarrow\ x_2\ =\ 8]


And finally:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_1\ =\ 7]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_5\ =\ 4]


The original number is then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 78134]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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